8.152   ODE No. 1742

$$\boxed{{\displaystyle 2\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-3{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+f\left(x\right){\left(y\left(x\right)\right)}^2=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 11.134414 (sec), leaf count = 30 $$\text{DSolve}[f(x)y(x{)}^2+2y(x)y^{″}(x)-3y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.140 (sec), leaf count = 60 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{2}-\frac{f\left(\mathit{\_}\mathit{a}\right)}{2}\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$